Journal of Function Spaces
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The latest articles from Hindawi Publishing Corporation
© 2015 , Hindawi Publishing Corporation . All rights reserved.

A Continuous Characterization of TriebelLizorkin Spaces Associated with Hermite Expansions
Thu, 28 May 2015 14:32:36 +0000
http://www.hindawi.com/journals/jfs/2015/104897/
We study the properties of the TriebelLizorkin spaces associated with the multidimensional Hermite expansions on (). In addition to the endpoint estimates, we give the continuous characterizations of these spaces via harmonic and thermic extensions from into . Based on this result, we obtain the boundedness of Riesz transform associated with the Hermite expansions.
Shuli Gong, Bolin Ma, and Zunwei Fu
Copyright © 2015 Shuli Gong et al. All rights reserved.

Fredholm Weighted Composition Operators on Weighted Banach Spaces of Analytic Functions of Type
Wed, 27 May 2015 09:05:14 +0000
http://www.hindawi.com/journals/jfs/2015/982135/
We study Fredholm (weighted) composition operators between general weighted Banach spaces of analytic functions on the open unit disc with supnorms.
M. Carmen GómezCollado and David Jornet
Copyright © 2015 M. Carmen GómezCollado and David Jornet. All rights reserved.

On Pointwise Approximation of Conjugate Functions by Some Hump Matrix Means of Conjugate Fourier Series
Tue, 26 May 2015 05:50:41 +0000
http://www.hindawi.com/journals/jfs/2015/470205/
The results generalizing some theorems on summability are shown. The same degrees of pointwise approximation as in earlier papers by weaker assumptions on considered functions and examined summability methods are obtained. From presented pointwise results, the estimation on norm approximation is derived. Some special cases as corollaries are also formulated.
W. Łenski and B. Szal
Copyright © 2015 W. Łenski and B. Szal. All rights reserved.

A Local Estimate for the Maximal Function in Lebesgue Spaces with EXPType Exponents
Thu, 21 May 2015 12:51:46 +0000
http://www.hindawi.com/journals/jfs/2015/581064/
It is proven that if in a bounded domain and if for some , then given , the HardyLittlewood maximal function of , , is such that . Because , the thesis is slightly weaker than for some . The assumption that for some is proven to be optimal in the framework of the Orlicz spaces to obtain in the same class of spaces.
Alberto Fiorenza
Copyright © 2015 Alberto Fiorenza. All rights reserved.

Fixed Point Theorems with Applications to the Solvability of Operator Equations and Inclusions on Function Spaces
Wed, 20 May 2015 13:36:23 +0000
http://www.hindawi.com/journals/jfs/2015/415950/
Nawab Hussain, Jesus GarciaFalset, MohamedAziz Taoudi, and Calogero Vetro
Copyright © 2015 Nawab Hussain et al. All rights reserved.

Recent Developments on Fixed Point Theory in Function Spaces and Applications to Control and Optimization Problems
Wed, 20 May 2015 08:26:57 +0000
http://www.hindawi.com/journals/jfs/2015/512564/
Hemant Kumar Nashine, Mujahid Abbas, Marlène Frigon, and Calogero Vetro
Copyright © 2015 Hemant Kumar Nashine et al. All rights reserved.

Hybrid SteepestDescent Methods for Triple Hierarchical Variational Inequalities
Tue, 19 May 2015 11:32:44 +0000
http://www.hindawi.com/journals/jfs/2015/980352/
We introduce and analyze a relaxed iterative algorithm by combining Korpelevich’s extragradient method, hybrid steepestdescent method, and Mann’s iteration method. We prove that, under appropriate assumptions, the proposed algorithm converges strongly to a common element of the fixed point set of infinitely many nonexpansive mappings, the solution set of finitely many generalized mixed equilibrium problems (GMEPs), the solution set of finitely many variational inclusions, and the solution set of general system of variational inequalities (GSVI), which is just a unique solution of a triple hierarchical variational inequality (THVI) in a real Hilbert space. In addition, we also consider the application of the proposed algorithm for solving a hierarchical variational inequality problem with constraints of finitely many GMEPs, finitely many variational inclusions, and the GSVI. The results obtained in this paper improve and extend the corresponding results announced by many others.
L. C. Ceng, A. Latif, C. F. Wen, and A. E. AlMazrooei
Copyright © 2015 L. C. Ceng et al. All rights reserved.

A LyapunovType Inequality for a Fractional Differential Equation under a Robin Boundary Condition
Tue, 19 May 2015 11:31:16 +0000
http://www.hindawi.com/journals/jfs/2015/468536/
We establish a new Lyapunovtype inequality for a class of fractional differential equations under Robin boundary conditions. The obtained inequality is used to obtain an interval where a linear combination of certain MittagLeffler functions has no real zeros.
Mohamed Jleli, Lakhdar Ragoub, and Bessem Samet
Copyright © 2015 Mohamed Jleli et al. All rights reserved.

Two Positive Solutions of ThirdOrder BVP with Integral Boundary Condition and SignChanging Green's Function
Tue, 19 May 2015 08:28:44 +0000
http://www.hindawi.com/journals/jfs/2015/491423/
We are concerned with the following thirdorder boundary value problem with integral boundary condition: where , and . Although the corresponding Green's function is signchanging, we still obtain the existence of at least two positive and decreasing solutions under some suitable conditions on by using the twofixedpoint theorem due to Avery and Henderson. An example is also included to illustrate the main results obtained.
BingWei Niu, JianPing Sun, and QiuYan Ren
Copyright © 2015 BingWei Niu et al. All rights reserved.

Some Results on Best Proximity Points of Cyclic Contractions in Probabilistic Metric Spaces
Tue, 19 May 2015 07:31:25 +0000
http://www.hindawi.com/journals/jfs/2015/470574/
This paper investigates properties of convergence of distances of cyclic contractions on the union of the subsets of an abstract set defining probabilistic metric spaces and Menger probabilistic metric spaces as well as the characterization of Cauchy sequences which converge to the best proximity points. The existence and uniqueness of fixed points and best proximity points of cyclic contractions defined in induced complete Menger spaces are also discussed in the case when the associate complete metric space is a uniformly convex Banach space. On the other hand, the existence and the uniqueness of fixed points of the composite mappings restricted to each of the subsets in the cyclic disposal are also investigated and some illustrative examples are given.
Manuel De la Sen and Erdal Karapınar
Copyright © 2015 Manuel De la Sen and Erdal Karapınar. All rights reserved.

Upper Semicontinuity of Solution Mappings to Parametric Generalized Vector Quasiequilibrium Problems
Mon, 18 May 2015 13:22:52 +0000
http://www.hindawi.com/journals/jfs/2015/764187/
We establish the upper semicontinuity of solution mappings for a class of parametric generalized vector quasiequilibrium problems. As applications, we obtain the upper semicontinuity of solution mappings to several problems, such as
parametric optimization problem, parametric saddle point problem, parametric Nash equilibria problem, parametric variational inequality, and parametric equilibrium problem.
Shuqiang Shan, Yu Han, and Nanjing Huang
Copyright © 2015 Shuqiang Shan et al. All rights reserved.

Existence of Positive Solutions for a FourthOrder Point Boundary Value Problem
Mon, 18 May 2015 12:06:52 +0000
http://www.hindawi.com/journals/jfs/2015/928105/
By using Krasnosel’skii’s fixed point theorem and the fixed point index theorem in the special function space, we obtain some sufficient conditions for the existence of positive solutions of fourthorder boundary value problem with multipoint boundary conditions. Applications of our results to some special problems are also discussed.
Liu Yang and Chunfang Shen
Copyright © 2015 Liu Yang and Chunfang Shen. All rights reserved.

Common Fixed Point of Two Weakly Commuting Mappings in Metric Spaces
Mon, 18 May 2015 12:06:27 +0000
http://www.hindawi.com/journals/jfs/2015/350840/
We prove some common fixed point results for two mappings satisfying generalized contractive condition in metric space. Note that metric of main results in this work are not necessarily continuous. So our results extend and improve several previous works. We also present one example that shows the applicability and usefulness of our results.
Poom Kumam, Wutiphol Sintunavarat, Shaban Sedghi, and Nabi Shobkolaei
Copyright © 2015 Poom Kumam et al. All rights reserved.

Boundary Value Problems of Fractional Order Differential Equation with Integral Boundary Conditions and Not Instantaneous Impulses
Mon, 18 May 2015 12:03:25 +0000
http://www.hindawi.com/journals/jfs/2015/954925/
We investigate the existence of mild solutions for fractional order differential equations with integral boundary conditions and not instantaneous impulses. By some fixedpoint theorems, we establish sufficient conditions for the existence and uniqueness of solutions. Finally, two interesting examples are given to illustrate our theory results.
Peiluan Li and Changjin Xu
Copyright © 2015 Peiluan Li and Changjin Xu. All rights reserved.

Some Generalized Difference Sequence Spaces Defined by a Sequence of Moduli in Normed Spaces
Mon, 18 May 2015 11:48:57 +0000
http://www.hindawi.com/journals/jfs/2015/413850/
We introduce some new generalized difference sequence spaces by means of ideal convergence, infinite matrix, and a sequence of modulus functions over normed spaces. We also make an effort to study several properties relevant to topological, algebraic, and inclusion relations between these spaces.
Abdullah Alotaibi, Kuldip Raj, and S. A. Mohiuddine
Copyright © 2015 Abdullah Alotaibi et al. All rights reserved.

On the Generalized UlamHyersRassias Stability of Quadratic Mappings in Modular Spaces without Conditions
Mon, 18 May 2015 10:49:31 +0000
http://www.hindawi.com/journals/jfs/2015/461719/
We approach the generalized UlamHyersRassias (briefly, UHR) stability of quadratic functional equations via the extensive studies of fixed point theory. Our results are obtained in the framework of modular spaces whose modulars are lower semicontinuous (briefly, lsc) but do not satisfy any relatives of conditions.
Kittipong Wongkum, Parin Chaipunya, and Poom Kumam
Copyright © 2015 Kittipong Wongkum et al. All rights reserved.

New Dependent Fixed Point Theorems for Suzuki Type Contractions
Mon, 18 May 2015 10:23:20 +0000
http://www.hindawi.com/journals/jfs/2015/136306/
We introduce new concepts of an GFcontractive nonselfmapping, a weak GFcontractive nonselfmapping, a generalized GFcontractive nonselfmapping, and Suzuki type GFcontractions and establish the existence of
PPF dependent fixed point theorems for such kind of contractive nonselfmappings in the Razumikhin class. As applications of our results, we derive some PPF dependent fixed point theorems for GFcontractive nonselfmappings whenever the range space is endowed with a graph or a partial order. The obtained results generalize, extend, and modify some PPF dependent fixed point results in the literature.
M. A. Kutbi, N. Hussain, and S. Khaleghizadeh
Copyright © 2015 M. A. Kutbi et al. All rights reserved.

On a New Faster Implicit Fixed Point Iterative Scheme in Convex Metric Spaces
Mon, 18 May 2015 09:54:18 +0000
http://www.hindawi.com/journals/jfs/2015/905834/
The purpose of this paper is to consider a new implicit iteration and study its strong convergence, stability, and data dependence. It is proved through numerical examples that newly introduced iteration has better convergence rate than well known implicit Mann iteration as well as implicit Ishikawa iteration and implicit iterations converge faster as compared to corresponding explicit iterations. Applications of implicit iterations to RNN (Recurrent Neural Networks) analysis are also presented.
Renu Chugh, Preety Malik, and Vivek Kumar
Copyright © 2015 Renu Chugh et al. All rights reserved.

Caristi’s Fixed Point Theorem and Subrahmanyam’s Fixed Point Theorem in Generalized Metric Spaces
Mon, 18 May 2015 08:56:55 +0000
http://www.hindawi.com/journals/jfs/2015/709391/
We discuss the completeness of generalized metric spaces
in the sense of Branciari.
We also prove generalizations
of Subrahmanyam’s and Caristi’s fixed point theorem.
Badriah Alamri, Tomonari Suzuki, and Liaqat Ali Khan
Copyright © 2015 Badriah Alamri et al. All rights reserved.

On the Approximate Controllability of Fractional Evolution Equations with Generalized RiemannLiouville Fractional Derivative
Mon, 18 May 2015 08:36:34 +0000
http://www.hindawi.com/journals/jfs/2015/263823/
We discuss the approximate controllability of fractional evolution equations involving generalized RiemannLiouville fractional derivative. The results are obtained with the help of the theory of fractional calculus, semigroup theory, and the Schauder fixed point theorem under the assumption that the corresponding linear system is approximately controllable.
Finally, an example is provided to illustrate the abstract theory.
N. I. Mahmudov and M. A. McKibben
Copyright © 2015 N. I. Mahmudov and M. A. McKibben. All rights reserved.

An Approximation Method for Solving Volterra Integrodifferential Equations with a Weighted Integral Condition
Wed, 13 May 2015 06:37:46 +0000
http://www.hindawi.com/journals/jfs/2015/758410/
We apply the reproducing kernel Hilbert space (RKHS) method
for getting analytical and approximate solutions for secondorder hyperbolic
integrodifferential equations with a weighted integral condition. The
analytical solution is represented in the form of series; thus, the nterms
approximate solutions are obtained. The results of the numerical examples
are compared with the exact solutions to illustrate the accuracy and the
effectivity of this method.
A. GuezaneLakoud, N. Bendjazia, and R. Khaldi
Copyright © 2015 A. GuezaneLakoud et al. All rights reserved.

Some Discussions on the Difference Equation
Sun, 10 May 2015 09:32:11 +0000
http://www.hindawi.com/journals/jfs/2015/737420/
We give in this work the sufficient conditions on the positive solutions of the difference equation , , where α, k, and under positive initial conditions , to be bounded, αconvergent, the equilibrium point to be globally asymptotically stable and that every positive solution converges to a prime twoperiodic solution. Our results coincide with that known for the cases of Amleh et al. (1999) and of Hamza and Morsy (2009). We offer improving conditions in the case of of Gümüs and Öcalan (2012) and explain our results by some numerical examples with figures.
Awad A. Bakery
Copyright © 2015 Awad A. Bakery. All rights reserved.

Positive Coexistence of Steady States for a Diffusive RatioDependent PredatorPrey Model with an Infected Prey
Wed, 06 May 2015 12:01:57 +0000
http://www.hindawi.com/journals/jfs/2015/810451/
We examine a diffusive ratiodependent predatorprey system with disease in the prey under homogeneous Dirichlet boundary conditions with a hostile environment at its boundary. We investigate the positive coexistence of three interacting species (susceptible prey, infected prey, and predator) and provide nonexistence conditions of positive solutions to the system. In addition, the global stability of the trivial and semitrivial solutions to the system is studied. Furthermore, the biological interpretation based on the result is also presented. The methods are employed from a comparison argument for the elliptic problem as well as the fixedpoint theory as applied to a positive cone on a Banach space.
Kwangjoong Kim and Inkyung Ahn
Copyright © 2015 Kwangjoong Kim and Inkyung Ahn. All rights reserved.

Approximative Compactness and RadonNikodym Property in Nearly Dentable Banach Spaces and Applications
Wed, 06 May 2015 09:41:31 +0000
http://www.hindawi.com/journals/jfs/2015/921456/
Authors define nearly dentable Banach space. Authors study RadonNikodym property, approximative compactness and continuity metric projector operator in nearly dentable space. Moreover, authors obtain some examples of nearly dentable space in Orlicz function spaces. Finally, by the method of geometry of Banach spaces, authors give important applications of nearly dentability in generalized inverse theory of Banach space.
Shaoqiang Shang and Yunan Cui
Copyright © 2015 Shaoqiang Shang and Yunan Cui. All rights reserved.

Sharp Power Mean Bounds for the OneParameter Harmonic Mean
Thu, 30 Apr 2015 18:45:29 +0000
http://www.hindawi.com/journals/jfs/2015/517647/
We present the best possible parameters and such that the double inequality holds for all and with , where and and are the power and oneparameter harmonic means of and , respectively.
YuMing Chu, LiMin Wu, and YingQing Song
Copyright © 2015 YuMing Chu et al. All rights reserved.

Solitary Waves of the Schrödinger Lattice System with Nonlinear Hopping
Wed, 29 Apr 2015 08:55:51 +0000
http://www.hindawi.com/journals/jfs/2015/385649/
This paper is concerned with the nonlinear Schrödinger lattice with nonlinear hopping. Via variation approach and the Nehari manifold argument, we obtain two types of solution: periodic ground state and localized ground state. Moreover, we consider the convergence of periodic solutions to the solitary waves.
Ming Cheng
Copyright © 2015 Ming Cheng. All rights reserved.

Iterative Methods for Nonconvex Equilibrium Problems in Uniformly Convex and Uniformly Smooth Banach Spaces
Tue, 28 Apr 2015 14:00:54 +0000
http://www.hindawi.com/journals/jfs/2015/346830/
We suggest and study the convergence of some new iterative schemes for solving nonconvex equilibrium problems in Banach spaces. Many existing results have been obtained as particular cases.
Messaoud Bounkhel
Copyright © 2015 Messaoud Bounkhel. All rights reserved.

Generalized Fractional Integral Operators on Generalized Local Morrey Spaces
Wed, 22 Apr 2015 06:23:08 +0000
http://www.hindawi.com/journals/jfs/2015/594323/
We study the continuity properties of the generalized fractional integral operator on the generalized local Morrey spaces and generalized Morrey spaces . We find conditions on the triple which ensure the Spannetype boundedness of from one generalized local Morrey space to another , , and from to the weak space , . We also find conditions on the pair which ensure the Adamstype boundedness of from to for and from to for . In all cases the conditions for the boundedness of are given in terms of Zygmundtype integral inequalities on and , which do not assume any assumption on monotonicity of , , and in .
V. S. Guliyev, A. F. Ismayilova, A. Kucukaslan, and A. Serbetci
Copyright © 2015 V. S. Guliyev et al. All rights reserved.

HardyLittlewoodSobolev Inequalities on Adic Central Morrey Spaces
Wed, 22 Apr 2015 06:19:59 +0000
http://www.hindawi.com/journals/jfs/2015/419532/
We establish the HardyLittlewoodSobolev inequalities on adic central Morrey spaces. Furthermore, we obtain the central BMO estimates for commutators of adic Riesz potential on adic central Morrey spaces.
Qing Yan Wu and Zun Wei Fu
Copyright © 2015 Qing Yan Wu and Zun Wei Fu. All rights reserved.

Characterization Theorems for Generalized Functionals of DiscreteTime Normal Martingale
Sun, 19 Apr 2015 10:42:18 +0000
http://www.hindawi.com/journals/jfs/2015/714745/
We aim at characterizing generalized functionals of discretetime normal martingales. Let be a discretetime normal martingale that has the chaotic representation property. We first construct testing and generalized functionals of with an appropriate orthonormal basis for ’s square integrable functionals. Then we introduce a transform, called the Fock transform, for these functionals and characterize them via the transform. Several characterization theorems are established. Finally we give some applications of these characterization theorems. Our results show that generalized functionals of discretetime normal martingales can be characterized only by growth condition, which contrasts sharply with the case of some continuoustime processes (e.g., Brownian motion), where both growth condition and analyticity condition are needed to characterize generalized functionals of those continuoustime processes.
Caishi Wang and Jinshu Chen
Copyright © 2015 Caishi Wang and Jinshu Chen. All rights reserved.